In this section, we discuss the effect of \(V(\phi )=\frac{\lambda }{3!}\phi ^{3}\)  interaction through the perturbative technique on the violation of NEC by quantum states under time evolution. In order to apply the perturbative technique, we follow the interaction picture of quantum field theory [1]}. Hence, the field operator can be expanded on a basis consists of mode solutions of free d'Alembert's equation in the following manner
\(\hat{\phi }(x)=\sum _{i}[\hat{a}_{i}g_{i}(x)+\hat{a}_{i}^{\dagger }g_{i}^{*}(x)],\) 
